A097282 Numbers k that are the hypotenuse of exactly 40 distinct integer-sided right triangles, i.e., k^2 can be written as a sum of two squares in 40 ways.

32045, 40885, 45305, 58565, 64090, 67405, 69745, 77285, 80665, 81770, 90610, 91205, 96135, 98345, 98605, 99905, 101065, 107185, 111605, 114985, 117130, 120445, 122655, 124865, 127465, 128180, 128945, 130645, 134810, 135915, 137605

Offset

1,1

Comments

k^2 is always the sum of k^2 and 0^2, but no real triangle can have a zero-length side. Thus, the Mathematica program below searches for length 41 and implicitly drops the zero-squared-plus-n-squared solution. - Harvey P. Dale, Dec 09 2010

If m is a term, then 2*m and p*m are terms where p is any prime of the form 4j+3. - Ray Chandler, Dec 30 2019

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[150000], Length[PowersRepresentations[#^2, 2, 2]]==41&] (* Harvey P. Dale, Dec 09 2010 *)

Crossrefs

Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084648 (4), A084649 (5), A097219 (6), A097101 (7), A290499 (8), A290500 (9), A097225 (10), A290501 (11), A097226 (12), A097102 (13), A290502 (14), A290503 (15), A097238 (16), A097239 (17), A290504 (18), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097626 (67).

Sequence in context: A156977 A217368 A359343 * A264499 A249230 A250897

Adjacent sequences: A097279 A097280 A097281 * A097283 A097284 A097285

Keyword

nonn

Author

James R. Buddenhagen, Sep 17 2004

Status

approved